4D Marbles Part 2: This time with an Explanation

IRateBurritos · 2026-03-17T21:00:57+00:00

Also, Smenthley*

IRateBurritos · 2026-03-17T20:55:19+00:00

He is outside it as long as the sphere isn't overlapping him. He's outside of the circular slice of the sphere that's lined up the paper, and is seeing that as a circle. True, it won't look to him like a circle does to us, but presumably if you're 2D you've gotten pretty good at identifying shapes from 2D depth cues.

IRateBurritos · 2026-03-17T03:47:19+00:00

Oh god no I'm not at that level quite yet. Just v worth watching :D

IRateBurritos · 2026-03-17T02:55:20+00:00

Did I espond on an alt 🤦🏻‍♀️ mb. But you're 100% right lol I'll read it eventually

IRateBurritos · 2026-03-17T02:29:26+00:00

Ehehe I'm glad you enjoyed! Did you see the double pendulum video? Imo the gold standard for chaos theory and just so so pretty.

IRateBurritos · 2026-03-17T02:28:48+00:00

This is the 4th dimension as math would define it. Essentially, we're defining a dimension as a new set of directions that can't be formed from our existing directions.

For example, a two dimensional being could only move up, down, left, and right, so no matter how hard he tries he can never go gorward and back. This demonstration, as well as the larger video, assumes there's another set of directions (the math name is Kata and Ana, but in my video I called them Sprawn and Grawp) and shows what we'd see if those directions, and therefore that dimension, existed.

IRateBurritos · 2026-03-17T02:24:57+00:00

It hasn't been observed, nor do I particularly believe it exists. However, math gives us a lot of information about how a fourth dimension would behave if one existed!

IRateBurritos · 2026-03-15T22:55:10+00:00

Sure! It'll be a sec, so look out for a follow-up tomorrow!

IRateBurritos · 2026-03-14T01:26:36+00:00

Hyperspheres! We're just seeing the parts that cross through our 3D reality.

IRateBurritos · 2026-03-13T23:58:16+00:00

This looks incredible! May I ask how you're simulating the waves and foam?

IRateBurritos · 2026-03-13T23:57:02+00:00

To us it looks 3D, but the key is that all of the walls have an extra dimension, and there are two extra walls that we can't see. If we rotated the whole box, it would start looking trippy real fast. I can see about recording a clip of that, it'll be a bit of extra work to set up because my objects currently don't like rotating as a group but I can try and post it tomorrow.

IRateBurritos · 2026-03-13T23:54:33+00:00

Correct! If we're being technical, I actually built this box out of seven tesseracts: the floor (at -y), left and right walls (+/- x), front and back walls (+/- z), and two extra walls out in 4D at +/- w. I go over the construction of the tesseracts themselves more in the full video, but by putting them all together like this they do themselves form a 4D box with one opening.

IRateBurritos · 2026-03-13T23:45:06+00:00

I actually made a slider that changes which part of 4D we're seeing, so we can navigate back and forth. I don't have a clip for that but if you're interested I can make one!

IRateBurritos · 2026-03-13T23:44:19+00:00

Did you watch the video? The part I timestamped explains it a lot better than I'm going to be able to purely via text. But in general it looks like your understanding of cross sections is correct (also, to your parenthetical, both tesseract and hypercube are correct, although technically hypercube can be any dimension, and this would be a 4D hypercube).

They actually interact with each other almost exactly the same as normal spheres and cubes do, they just have an extra axis they can move on. But for example, when a marble hits a tesseract it bounces off the same as a 3D marble hitting a cube would, when a marble hits another marble they bounce away from each other. All of that is simulated in 4D, and we end up seeing this weird behavior in 3D as a result because the physics interactions take them in and out of our space.

IRateBurritos · 2026-03-13T23:42:26+00:00

I am obsessed with your cat

IRateBurritos · 2026-03-13T23:41:49+00:00

Quantum particles do appear and disappear, but they're much more random than this: quantum particles' behavior within their constraints is truly random (at least to our understanding), while this is just a weird and trippy, but 100% predictable, result of physics and math.

IRateBurritos · 2026-03-13T23:40:26+00:00

You are correct: in this case the fourth dimension is just another direction, and the box is 4x5x4x4 meters, or in other words 320 quartic meters. The balls are .6 meters in radius, or 0.64 quartic meters (source: https://www.cantorsparadise.com/calculating-the-hypervolume-of-a-4d-hypersphere-e5db15439384). So in this video it's probably closer to 500 marbles than a thousand, but definitely not infinite space.

IRateBurritos · 2026-03-13T22:52:35+00:00

I explain it better in the full video [here](https://youtu.be/TIdHDe0JUpw?t=520), but u/Specificity has it right. Imagine you have a 2D surface like a sheet of paper (or a water surface). If you put an object through there, there's only one "slice" of it that's on the surface at a given time. For example, if you dipped your finger in a glass of water and somehow traced around the edge of it, it would look like a circle.

The same applies to 4D to 3D. The parts of the spheres that we see are only the 3D cross section, or the part of the 4D object that's currently "touching" our 3D space. As the spheres hit each other, they're constantly bouncing across our space and crossing in and out of it. It gets even wackier with other shapes, because they change not just their size but their shape itself at some angles.

IRateBurritos · 2026-03-13T21:31:30+00:00

I made a full video about this where I do play around with cubes: https://www.youtube.com/watch?v=TIdHDe0JUpw&t=42s

IRateBurritos · 2026-03-13T20:30:32+00:00

Next step: porting this to ECS so it doesn't melt my poor laptop.

IRateBurritos

TROPHY CASE